What is the slope of the line?
1 answer:
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Answer:
Vertex = (1.4375, 37.0625)
Axis of symmetry: t = 1.4375
x-intercept: (2.9595, 0)
y-intercept: (0, 4)
another point: (2, 32)
Step-by-step explanation:
Given function:
(where h is the height in feet and t is the time in seconds)
The vertex is the turning point of the parabola.
To find the x-value of the turning point, differentiate the function:
Set it to zero:
Solve for t:
Input found value of t into the function to find the y-value of the vertex:
Therefore, the vertex is or (1.4375, 37.0625) in decimal form.
The axis of symmetry is the x-value of the vertex.
To find the x-intercepts, use the quadratic formula.
<u>Quadratic Formula</u>
As time is positive,
The y-intercept is when t = 0:
So the curve intercepts the y-axis at (0, 4)
Because of the modelling of the function, there will be a restricted domain: 0 ≤ t ≤ 2.9595
Therefore, to find another point, input a value in the domain into the function and solve:
⇒ (2, 32)
